Question

the equation of a circle is given below. identify the radius and center. then graph the circle. x²+(y + 3)²=25 radius: center: ()

Explanation:

Step1: Recall circle - equation formula

The standard form of the equation of a circle is $(x - a)^{2}+(y - b)^{2}=r^{2}$, where $(a,b)$ is the center of the circle and $r$ is the radius.

Step2: Rewrite the given equation

The given equation is $x^{2}+(y + 3)^{2}=25$, which can be written as $(x - 0)^{2}+(y-(-3))^{2}=5^{2}$.

Step3: Identify the center and radius

Comparing with the standard - form $(x - a)^{2}+(y - b)^{2}=r^{2}$, we have $a = 0$, $b=-3$, and $r = 5$. So the center of the circle is $(0,-3)$ and the radius is 5.

Answer:

Radius: 5
Center: (0, - 3)